Question

Find the exact value of the given expression (attached). I keep ending up with (√3 +1)/(2), but the answer choices are:
A. -1/2
B. (√3)/(2)
C. (√3 + 1)/(2√2)
D. (√3)/(3)
E. (√3 - 1)/(2√2)

Answer 1

did you use half angle identity for the tan 17pi/12?

Answer 2

\[\Large \frac{\tan\left(\frac{17\pi}{12}\right)-\tan\left(\frac{\pi}{4}\right)}{1 + \tan\left(\frac{17\pi}{12}\right)\tan\left(\frac{\pi}{4}\right)}\]


\[\Large \tan\left(\frac{17\pi}{12}-\frac{\pi}{4}\right)\]


\[\Large \tan\left(\frac{17\pi}{12}-\frac{3\pi}{12}\right)\]


\[\Large \tan\left(\frac{17\pi-3\pi}{12}\right)\]


\[\Large \tan\left(\frac{14\pi}{12}\right)\]


\[\Large \tan\left(\frac{7\pi}{6}\right)\]


\[\Large \frac{\sqrt{3}}{3}\]



So \[\Large \frac{\tan\left(\frac{17\pi}{12}\right)-\tan\left(\frac{\pi}{4}\right)}{1 + \tan\left(\frac{17\pi}{12}\right)\tan\left(\frac{\pi}{4}\right)} = \frac{\sqrt{3}}{3}\]



Note: use the unit circle to do the last step.

Answer 3

Ohh... i get it. Thank you for your help!

Answer 4

yw